Soviet people truly considered taxis a bourgeois luxury.
And they certainly didn’t take a taxi to the bakery around the corner, as the character from Leonid Gaidai’s cult Soviet comedy The Diamond Arm famously said.
Compare this: a taxi fare was about 10 kopecks per kilometer, while a ride on public transport cost only 3-5 kopecks per trip. The average Soviet salary was 150-170 rubles.
Taxi drivers were considered something of a privileged class. They earned a decent wage and could drive luxurious Volga cars, and before the war, for example, they even drove ZIS-101 limousines.
You could "hail" a taxi if the green "available" sign was lit on the roof, or you could call for one by phone. However, the service was not very reliable.
Taxis were often used to get to or from the airport due to the limited availability of other transport options. Air travel back then wasn’t as popular as it is today.
There were people who only rode in a taxi a few times in their lives. For example, to pick up a wife from the maternity hospital, or after a big banquet, the person celebrating a milestone birthday might take a taxi home.